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Abstract:

An acoustic resonator comprises (a) a substrate having atop surface and a
bottom surface, a first end portion and an opposite, second end portion,
and a body portion defined therebetween; (b) an acoustic mirror having a
top surface and a bottom surface, a first end portion and an opposite,
second end portion, and a body portion defined therebetween, wherein the
bottom surface is formed on the top surface of the substrate; (c) a first
electrode having a top surface and a bottom surface, a first end portion
and an opposite, second end portion, and a body portion defined
therebetween, wherein the bottom surface is formed on the top surface of
the acoustic mirror; (d) a piezoelectric layer having a top surface and a
bottom surface, a first end portion and an opposite, second end portion,
and a body portion defined therebetween, wherein the bottom surface is
formed on the top surface of the first electrode; and (e) a second
electrode having a top surface and a bottom surface, a first end portion
and an opposite, second end portion, and a body portion defined
therebetween. The bottom surface is formed on the top surface of the
piezoelectric layer, wherein the overlapped area of body portions of the
substrate, the acoustic mirror, the first electrode, the piezoelectric
layer and the second electrode is defined as an active area A.

Claims:

1. A piezoelectric resonator structure, comprising: (a) a substrate
having a top surface and a bottom surface, a first end portion and an
opposite, second end portion, and a body portion defined therebetween;
(b) an acoustic mirror having a top surface and a bottom surface, a first
end portion and an opposite, second end portion, and a body portion
defined therebetween, wherein the bottom surface is formed on the top
surface of the substrate; (c) a first electrode having a top surface and
a bottom surface, a first end portion and an opposite, second end
portion, and a body portion defined therebetween, wherein the bottom
surface is formed on the top surface of the acoustic mirror; (d) a
piezoelectric layer having a top surface and a bottom surface, a first
end portion and an opposite, second end portion, and a body portion
defined therebetween, wherein the bottom surface is formed on the top
surface of the first electrode; and (e) a second electrode having a top
surface and a bottom surface, a first end portion and an opposite, second
end portion, and a body portion defined therebetween, wherein the bottom
surface is formed on the top surface of the piezoelectric layer, wherein
the overlapped area of body portions of the substrate, the acoustic
mirror, the first electrode, the piezoelectric layer and the second
electrode is defined as an active area A.

2. The piezoelectric resonator structure of claim 1, further comprising a
first interference structure extending from the first end portion of the
second electrode, and a second interference structure extending from the
second end portion of the second electrode, wherein a first air gap is
formed in the first end portion of the piezoelectric layer and a second
air gap is formed in the second end portion of the piezoelectric layer.

3. The piezoelectric resonator structure of claim 2, wherein a first
interference structure extending from the first end portion of the second
electrode, and a second interference structure extending from the second
end portion of the second electrode, are positioned on top of the first
air gap and the second air gap, respectively.

4. The piezoelectric resonator structure of claim 1, wherein a first
interference structure having a first end portion and a second end
portion, is positioned on the top surface of the second electrode with
the second end portion sitting at the first end portion of the second
electrode and the first end portion suspended over the active area to
form a first air gap, and a second interference structure having a first
end portion and a second end portion, is positioned on the top surface of
the second electrode with the second end portion sitting at the second
end portion of the second electrode and the first end portion suspended
over the active area to form a second air gap.

5. The piezoelectric resonator structure of claim 1, wherein a first
interference structure having a first end portion and a second end
portion, is positioned on the top surface of the second electrode with
the second end portion at the first end portion of the second electrode
and the first end portion suspended over the first end portion of the
second electrode and the first end portion of the piezoelectric layer to
form a first air gap, and a second interference structure having a first
end portion and a second end portion, is positioned on the top surface of
the second electrode with the second end portion at the second end
portion of the second electrode and the first end portion suspended over
the second end portion of the second electrode and the second end portion
of the piezoelectric layer to form a second air gap.

6. The piezoelectric resonator structure of claim 1, wherein a first
trapezoid interference structure having a first end portion and a second
end portion, is positioned such that the first end portion is placed on
the top surface of the first end portion of the second electrode, and the
second end portion is placed on the top surface of the first end portion
of the piezoelectric layer so as to define a first air gap, and a second
trapezoid interference structure having a first end portion and a second
end portion, is positioned such that the first end portion is placed on
the top surface of the second end portion of the second electrode and the
second end portion is placed on the top surface of the second end portion
of the piezoelectric layer so as to define a second air gap.

7. The piezoelectric resonator structure of claim 1, wherein a first end
portion of the second electrode is made in an arch shape on the top
surface of the piezoelectric layer to form a first air gap, and a second
end portion of the second electrode is made in an arch shape on the top
surface of the piezoelectric layer to form a second air gap.

8. The piezoelectric resonator structure of claim 1, wherein the top
surface of the second electrode is covered with a dielectric layer to
form a multi-layered structure having a first end portion and a second
end portion, and the first end portion of the multi-layered structure is
made in an arch shape on the top surface of the piezoelectric layer to
form a first air gap, and the second end portion of the multi-layered
structure is made in an arch shape on the top surface of the
piezoelectric layer to form a second air gap.

Description:

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application is a continuation application under 37
C.F.R. §1.53(b) of U.S. patent application Ser. No. 12/626,035 filed
on Nov. 25, 2009, naming John Choy, et al. as inventors. Priority under
35 U.S.C. §120 is claimed from U.S. patent application Ser. No.
12/626,035, and the entire disclosure of U.S. patent application Ser. No.
12/626,035 is specifically incorporated herein by reference.

[0002] The present application is also a continuation-in-part of and
claims priority under 35 U.S.C. §120 from U.S. patent application
Ser. No. 12/490,525 entitled "ACOUSTIC RESONATOR STRUCTURE COMPRISING A
BRIDGE" to John Choy, et al. and filed on Jun. 24, 2009. The disclosure
of this application is specifically incorporated herein by reference.

BACKGROUND

[0003] In many electronic applications, electrical resonators are used.
For example, in many wireless communications devices, radio frequency
(rf) and microwave frequency resonators are used as filters to improve
reception and transmission of signals. Filters typically include
inductors and capacitors, and more recently resonators.

[0004] As will be appreciated, it is desirable to reduce the size of
components of electronic devices. Many known filter technologies present
a barrier to overall system miniaturization. With the need to reduce
component size, a class of resonators based on the piezoelectric effect
has emerged. In piezoelectric-based resonators, acoustic resonant modes
are generated in the piezoelectric material. These acoustic waves are
converted into electrical waves for use in electrical applications.

[0005] One type of piezoelectric resonator is a Film Bulk Acoustic
Resonator (FBAR). The FBAR has the advantage of small size and lends
itself to Integrated Circuit (IC) manufacturing tools and techniques. The
FBAR includes an acoustic stack comprising, inter alia, a layer of
piezoelectric material disposed between two electrodes. Acoustic waves
achieve resonance across the acoustic stack, with the resonant frequency
of the waves being determined by the materials in the acoustic stack.

[0006] FBARs are similar in principle to bulk acoustic resonators such as
quartz, but are scaled down to resonate at GHz frequencies. Because the
FBARs have thicknesses on the order of microns and length and width
dimensions of hundreds of microns, FBARs beneficially provide a
comparatively compact alternative to known resonators.

[0007] Desirably, the bulk acoustic resonator excites only
thickness-extensional (TE) modes, which are longitudinal mechanical waves
having propagation (k) vectors in the direction of propagation. The TE
modes desirably travel in the direction of the thickness (e.g.,
z-direction) of the piezoelectric layer.

[0008] Unfortunately, in addition to the desired TE modes there are
lateral modes, known as Rayleigh-Lamb modes, generated in the acoustic
stack as well. The Rayleigh-Lamb modes are mechanical waves having
k-vectors that are perpendicular to the direction of TE modes, the
desired modes of operation. These lateral modes travel in the areal
dimensions (x, y directions of the present example) of the piezoelectric
material. Among other adverse effects, lateral modes deleteriously impact
the quality (Q) factor of an FBAR device. In particular, the energy of
Rayleigh-Lamb modes is lost at the interfaces of the FBAR device. As will
be appreciated, this loss of energy to spurious modes is a loss in energy
of desired longitudinal modes, and ultimately a degradation of the
Q-factor.

[0009] What is needed, therefore, is an acoustic resonator that overcomes
at least the known shortcomings described above.

SUMMARY

[0010] In accordance with a representative embodiment, a piezoelectric
resonator structure, comprises: (a) a substrate having atop surface and a
bottom surface, a first end portion and an opposite, second end portion,
and a body portion defined therebetween; (b) an acoustic minor having a
top surface and a bottom surface, a first end portion and an opposite,
second end portion, and a body portion defined therebetween, wherein the
bottom surface is formed on the top surface of the substrate; (c) a first
electrode having a top surface and a bottom surface, a first end portion
and an opposite, second end portion, and a body portion defined
therebetween, wherein the bottom surface is formed on the top surface of
the acoustic mirror; (d) a piezoelectric layer having a top surface and a
bottom surface, a first end portion and an opposite, second end portion,
and a body portion defined therebetween, wherein the bottom surface is
formed on the top surface of the first electrode; and (e) a second
electrode having a top surface and a bottom surface, a first end portion
and an opposite, second end portion, and a body portion defined
therebetween. The bottom surface is formed on the top surface of the
piezoelectric layer, wherein the overlapped area of body portions of the
substrate, the acoustic mirror, the first electrode, the piezoelectric
layer and the second electrode is defined as an active area A.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The illustrative embodiments are best understood from the following
detailed description when read with the accompanying drawing figures. It
is emphasized that the various features are not necessarily drawn to
scale. In fact, the dimensions may be arbitrarily increased or decreased
for clarity of discussion. Wherever applicable and practical, like
reference numerals refer to like elements.

[0012] FIG. 1A shows a cross-sectional view of an acoustic resonator in
accordance with a representative embodiment.

[0013] FIG. 1B shows atop view of an acoustic resonator in accordance with
a representative embodiment.

[0014] FIG. 2A shows a graph of the Q-factor at parallel resonance
(Qp) versus width of the cantilevered portion(s) of an acoustic
resonator in accordance with a representative embodiment.

[0015] FIG. 2B shows a graph of the Q-factor at series resonance (Qs)
versus width of the cantilevered portion(s) of an acoustic resonator in
accordance with a representative embodiment.

[0016] FIG. 3 shows a cross-sectional view of an acoustic resonator in
accordance with a representative embodiment.

[0017] FIG. 4A shows a graph of the Q-factor at parallel resonance
(Qp) versus width of the cantilevered portion(s) of an acoustic
resonator in accordance with a representative embodiment.

[0018] FIG. 4B shows a graph of the Q-factor at series resonance (Qs)
versus width of the cantilevered portion(s) of an acoustic resonator in
accordance with a representative embodiment.

[0019] FIG. 4C shows a graph of the Q-factor at parallel resonance
(Qp) versus width of the cantilevered portion(s) of an acoustic
resonator in accordance with a representative embodiment.

[0020] FIG. 5A shows a cross-sectional view of an acoustic resonator in
accordance with a representative embodiment taken along line 5A-5A in
FIG. 5B.

[0021] FIG. 5B shows a top view of an acoustic resonator in accordance
with a representative embodiment.

[0022] FIG. 6 shows a cross-sectional view of an acoustic resonator in
accordance with a representative embodiment.

[0023] FIG. 7 shows a simplified schematic diagram of an electrical filter
in accordance with a representative embodiment.

DEFINED TERMINOLOGY

[0024] It is to be understood that the terminology used herein is for
purposes of describing particular embodiments only, and is not intended
to be limiting. The defined terms are in addition to the technical and
scientific meanings of the defined terms as commonly understood and
accepted in the technical field of the present teachings.

[0025] As used in the specification and appended claims, the terms `a`,
`an` and `the` include both singular and plural referents, unless the
context clearly dictates otherwise. Thus, for example, `a device`
includes one device and plural devices.

[0026] As used in the specification and appended claims, and in addition
to their ordinary meanings, the terms `substantial` or `substantially`
mean to with acceptable limits or degree. For example, `substantially
cancelled` means that one skilled in the art would consider the
cancellation to be acceptable.

[0027] As used in the specification and the appended claims and in
addition to its ordinary meaning, the term `approximately` means to
within an acceptable limit or amount to one having ordinary skill in the
art. For example, `approximately the same` means that one of ordinary
skill in the art would consider the items being compared to be the same.

DETAILED DESCRIPTION

[0028] In the following detailed description, for purposes of explanation
and not limitation, specific details are set forth in order to provide a
thorough understanding of illustrative embodiments according to the
present teachings. However, it will be apparent to one having ordinary
skill in the art having had the benefit of the present disclosure that
other embodiments according to the present teachings that depart from the
specific details disclosed herein remain within the scope of the appended
claims. Moreover, descriptions of well-known apparati and methods may be
omitted so as to not obscure the description of the illustrative
embodiments. Such methods and apparati are clearly within the scope of
the present teachings.

[0029] Generally, it is understood that the drawings and the various
elements depicted therein are not drawn to scale. Further, relative
terms, such as "above," "below," "top," "bottom," "upper" and "lower" are
used to describe the various elements' relationships to one another, as
illustrated in the accompanying drawings. It is understood that these
relative terms are intended to encompass different orientations of the
device and/or elements in addition to the orientation depicted in the
drawings. For example, if the device were inverted with respect to the
view in the drawings, an element described as "above" another element,
for example, would now be below that element.

[0030] FIG. 1A is a cross-sectional view along the line 1B-1B of an
acoustic resonator 100 in accordance with a representative embodiment.
Illustratively, the acoustic resonator 100 comprises an FBAR. The
acoustic resonator 100 comprises a substrate 101, a first electrode 102
disposed beneath a piezoelectric layer 103, which comprises a first
surface in contact with a first electrode 102 and a second surface in
contact with a second electrode 104. An optional passivation layer 105 is
provided over the second electrode 104. A cantilevered portion 106 of the
second electrode 104 is provided on at least one side of the second
electrode 104. The cantilevered portion 106 may also be referred to as a
`wing.`

[0031] The acoustic resonator 100 may be fabricated according to known
semiconductor processing methods and using known materials.
Illustratively, the acoustic resonator 100 may be fabricated according to
the teachings of commonly owned U.S. Pat. Nos. 5,587,620; 5,873,153;
6,384,697; 6,507,983; and 7,275,292 to Ruby, et al.; and 6,828,713 to
Bradley, et al. The disclosures of these patents are specifically
incorporated herein by reference. It is emphasized that the methods and
materials described in these patents are representative and other methods
of fabrication and materials within the purview of one of ordinary skill
in the art are contemplated.

[0032] When connected in a selected topology, a plurality of acoustic
resonators 100 can act as an electrical filter. For example, the acoustic
resonators 100 may be arranged in a ladder-filter arrangement, such as
described in U.S. Pat. No. 5,910,756 to Ella, and U.S. Pat. No. 6,262,637
to Bradley, et al., the disclosures of which are specifically
incorporated herein by reference. The electrical filters may be used in a
number of applications, such as in duplexers.

[0033] The first and second electrodes 102, 104 each comprise an
electrically conductive material (e.g., molybdenum (Mo)) and provide an
oscillating electric field in the y-direction of the coordinate system
shown (i.e., the direction of the thickness of the piezoelectric layer
103). In the illustrative embodiment described presently, the y-axis is
the axis for the TE (longitudinal) mode(s) for the resonator. In a
representative embodiment, the piezoelectric layer 103 and first and
second electrodes 102,104 are suspended over a cavity 107 formed by
selective etching of the substrate 101. The cavity 107 may be formed by a
number of known methods, for example as described in referenced commonly
owned U.S. Pat. No. 6,384,697 to Ruby, et al. Accordingly, the acoustic
resonator 100 is a mechanical resonator, which can be electrically
coupled via the piezoelectric layer 103. Other configurations that foster
mechanical resonance by FBARs are contemplated. For example, the acoustic
resonator 100 can be located over an acoustic mirror, such as a
mismatched acoustic Bragg reflector (not shown) formed in or on the
substrate 101. FBARs provided over an acoustic mirror are sometimes
referred to as solid mount resonators (SMRs) and, for example, may be as
described in U.S. Pat. No. 6,107,721 to Lakin, the disclosure of which is
specifically incorporated into this disclosure by reference in its
entirety.

[0034] The cantilevered portion 106 of the second electrode 104 extends
over a gap 108, which illustratively comprises air. In a representative
embodiment, a sacrificial layer (not shown) is deposited by known
technique over the first electrode 102 and a portion of the piezoelectric
layer 103. The second electrode 104 and passivation layer 105 are
provided over the sacrificial layer. Illustratively, the sacrificial
material comprises phosphosilicate glass (PSG), which illustratively
comprises 8% phosphorous and 92% silicon dioxide. After the formation of
the second electrode 104 and passivation layer 105, the sacrificial layer
is etched away illustratively with hydrofluoric acid leaving the
cantilevered portion 106. In a representative embodiment, the sacrificial
layer provided to form the cantilevered portion 106 and the sacrificial
layer provided to form the cavity 107 are removed in the same process
step.

[0035] Notably, rather than air, the gap 108 may comprise other materials
including tow acoustic impedance materials, such as carbon (C) doped
SiO2, which is also referred as Black-diamond; or dielectric resin
commercially known as SiLK; or benzocyclobutene (BCB). Such low acoustic
impedance materials may be provided in the gap 108 by known methods. The
low acoustic impedance material may be provided after removal of
sacrificial material used to form the gap 108, or may be used instead of
the sacrificial material in the gap 108, and not removed.

[0036] The region of contacting overlap of the first and second electrodes
102, 104, the piezoelectric layer 103 and the cavity 107, or other
reflector (e.g., Bragg reflector (not shown)) is referred to as an active
area 110 of the acoustic resonator 100. By contrast, an inactive area of
the acoustic resonator 100 comprises a region of overlap between first
electrode 102 or second electrode 104, or both, and the piezoelectric
layer 103 not disposed aver the cavity 107, or other suspension
structure, or acoustic mirror. As described more fully in the parent
application, it is beneficial to the performance of the acoustic
resonator 100 to reduce the area of the inactive region of the acoustic
resonator 100 to the extent practical.

[0037] The cantilevered portion 106 extends beyond an edge of the active
area 110 by a width 109 as shown. An electrical contact 111 is connected
to a signal line (not shown) and electronic components (not shown)
selected for the particular application of the acoustic resonator 100.
This portion of the acoustic resonator 100 comprises an interconnection
side 112 of the acoustic resonator 100. As will become clearer as the
present description continues, the interconnection side 112 of the second
electrode 104 to which the electrical contact 111 is made does not
comprise a cantilevered portion. By contrast, one or more non-connecting
sides 113 of the acoustic resonator 100 may comprise cantilevered
portions 106 that extend beyond the edge of the active area 110.

[0038] FIG. 1B shows a top view of the acoustic resonator 100 shown in
cross-sectional view in FIG. 1A and in accordance with a representative
embodiment. The acoustic resonator 100 also comprises the second
electrode 104 with the optional passivation layer 105 disposed thereover.
The second electrode 104 of the present embodiment is illustratively
apodized to reduce acoustic losses. Further details of the use of
apodization in acoustic resonators may be found in commonly owned U.S.
Pat. No. 6,215,375 to Larson III, et al; or in commonly owned U.S. Patent
Application Publication 20070279153 entitled "Piezoelectric Resonator
Structures and Electrical Filters" filed May 31, 2006, to Richard C.
Ruby. The disclosures of this patent and patent application publication
are specifically incorporated herein by reference in their entirety.

[0039] The second electrode 104 comprises non-connecting sides 113 and
interconnection side 112. In a representative embodiment, cantilevered
portions 106 are provided along each non-contacting side 113 and have the
same width. This is merely illustrative, and it is contemplated that at
least one side 113, but not all comprise a cantilevered portion 106.
Furthermore, it is contemplated that the second electrode 104 comprises
more or fewer than four sides as shown. For example, a pentagonal-shaped
second electrode is contemplated comprising four sides with cantilevered
portions on one or more of the sides, and the fifth side providing the
interconnection side. In a representative embodiment, the shape of the
first electrode 102 is substantially identical to the shape of the second
electrode 104. Notably, the first electrode 102 may comprise a larger
area than the second electrode 104, and the shape of the first electrode
102 may be different than the shape of the second electrode 104.

[0040] The fundamental mode of the acoustic resonator 100 is the
longitudinal extension mode or "piston" mode. This mode is excited by the
application of a time-varying voltage to the two electrodes at the
resonant frequency of the acoustic resonator 100. The piezoelectric
material converts energy in the form of electrical energy into mechanical
energy. In an ideal FBAR having infinitesimally thin electrodes,
resonance occurs when the applied frequency is equal to the velocity of
sound of the piezoelectric medium divided by twice the thickness of the
piezoelectric medium: f=vac/(2*T), where T is the thickness of the
piezoelectric medium and vac is the acoustic phase velocity. For
resonators with finite thickness electrodes, this equation is modified by
the weighted acoustic velocities and thicknesses of the electrodes.

[0041] A quantitative and qualitative understanding of the Q of a
resonator may be obtained by plotting on a Smith Chart the ratio of the
reflected energy to applied energy as the frequency is varied for the
case in which one electrode is connected to ground and another to signal,
for an FBAR resonator with an impedance equal to the system impedance at
the resonant frequency. As the frequency of the applied energy is
increased, the magnitude/phase of the FBAR resonator sweeps out a circle
on the Smith Chart. This is referred to as the Q-circle. Where the
Q-circle first crosses the real axes (horizontal axes), this corresponds
to the series resonance frequency fs. The real impedance as measured
in Ohms) is Rs. As the Q-circle continues around the perimeter of
the Smith chart, it again crosses the real axes. The second point at
which the Q circle crosses the real axis is labeled fp, the parallel
or anti-resonant frequency of the FBAR. The real impedance at fp is
Rp.

[0042] Often it is desirable to minimize Rs while maximizing Rp.
Qualitatively, the closer the Q-circle "hugs" the outer rim of the Smith
chart, the higher the Q-factor of the device. The Q-circle of an ideal
lossless resonator would have a radius of one and would be at the edge of
the Smith chart. However, as noted above, there are energy losses that
impact the Q-factor of the device. For instance, and in addition to the
sources of acoustic losses mentioned above, Rayleigh-Lamb (lateral or
spurious) modes are in the x,y dimensions of the piezoelectric layer 103.
These lateral modes are due to interfacial mode conversion of the
longitudinal mode traveling in the z-direction; and due to the creation
of non-zero propagation vectors, kx and ky, for both the TE
mode and the various lateral modes (e.g., the S0 (symmetric) mode and the
zeroth and (asymmetric) modes, A0 and A1), which are due to the
difference in effective velocities between the regions where electrodes
are disposed and the surrounding regions of the resonator where there are
no electrodes. At a specific frequency, the acoustic wave length of an
acoustic resonator is determined by v/f where v is acoustic velocity and
f is frequency. It is believed that periodicity of Qp (i.e., the position
of maxima and minima as a function of the width 109 of the cantilevered
portion 106) is related to the acoustic wave length. At a maxima of Qp,
the vibration of the wing 106 is comparatively far from its mechanical
resonance; while at a minima mechanical resonance of the cantilevered
portion 106 occurs. This phenomenon can be appreciated from a review of
FIG. 2A below, for example: as frequency decreases, acoustic wave length
increases, and the width 109 of the cantilevered portion 106 at a maxima
increases accordingly.

[0043] Regardless of their source, the lateral modes are parasitic in many
resonator applications. For example, the parasitic lateral modes couple
at the perimeter of the resonator and remove energy available for the
longitudinal modes and thereby reduce the Q-factor of the resonator
device. Notably, as a result of parasitic lateral modes and other
acoustic losses sharp reductions in Q can be observed on a Q-circle of
the Smith Chart of the parameter. These sharp reductions in Q-factor are
known as "rattles" or "loop-de-loops," which are shown and described
below.

[0044] The cantilevered portion(s) 106 of the representative embodiments
provide a change in the acoustic impedance at the boundary of the active
area 110 of the acoustic resonator 100. As a result, reflections of
lateral modes at the boundary are promoted. In a representative
embodiment, the boundary of the active area 110 of the acoustic resonator
100 and the cantilevered portion 106 is solid (first and second
electrodes 102, 104 and piezoelectric layer 103) and air, which presents
a comparatively large impedance mismatch and a comparatively high
reflection coefficient. As a result, lateral modes are comparatively
highly reflected, which improves the Q-factor by two mechanisms. First,
because the reflected lateral modes are not transmitted, their energy is
not lost. Improving the losses by reducing transmission of lateral modes
outside the active area 110 of the acoustic resonator 100 can increase
the Q-factor of the acoustic resonator 100. Second, a portion of the
reflected lateral modes is converted into desired longitudinal modes. The
greater the wave energy is in longitudinal modes, the higher the
Q-factor. As a result, the cantilevered portion(s) 106 of the acoustic
resonator 100 enhances the Q-factor of both the parallel and the series
resonance (i.e., Qp and Qs).

[0045] FIG. 2A shows a graph 200 of the Q-factor at parallel resonance
(Qp) versus width (e.g., width 109, also referred to as "wing
width") of the cantilevered portion(s) 106 ("wings") of an acoustic
resonator in accordance with a representative embodiment. The graph 200
provides data of an acoustic resonator comprising three cantilevered
portions 106, such as illustratively shown in FIGS. 1A and 1B. The
Q-factor is dependent on the width of the cantilevered portion 106 for a
given parallel resonance frequency. As shown, there are relative maxima
in Qp at points 201, 202 and 203; and local minima at points 204,
205 and 206 as the width 109 increases. Notably, Qp improves
significantly at a certain width 109, compared with width 109 of the
cantilevered portion 106 being zero, which is equivalent to an acoustic
resonator having substantially the same structure as acoustic resonator
100 but not comprising the cantilevered portion 106.

[0046] Improvements in Qp due to the inclusion of the cantilevered
portion 106 results from different boundary conditions at the edge of the
active area 110 of the acoustic resonator 100 compared to an acoustic
resonator not comprising a cantilevered portion(s). As described above,
the cantilevered portion 106 at the edge of active area 110 of the
acoustic resonator 100 will reflect certain acoustic modes due to the
impedance mismatch at the boundary of the cantilevered portion 106 and
the active area 110, resulting in improved Q. It is believed that the
local minima may result from the excitation of a mechanical resonance of
the cantilevered portion 106, which results in losses. The excited
resonance conditions at relative minima (points 204, 205, 206), result in
energy not reflected back into the active area 110 of the acoustic
resonator 100, losses and reduced Q. Accordingly, when designing acoustic
resonator 100, the width 109 of the cantilevered portion 106 is
beneficially selected at a relative maximum (points 201, 202, 203), and
not at a relative minimum (points 204, 205, 206).

[0047] FIG. 2B shows a graph 207 of the Q-factor at series resonance
(Qs) versus width (e.g., width 109 (`wing width`)) of the
cantilevered portion 106 (`wing`) of an acoustic resonator in accordance
with a representative embodiment. The graph 207 provides data of an
acoustic resonator comprising three cantilevered portions 106, such as
illustratively shown in FIGS. 1A and 1B. The Q-factor is dependent on the
width 109 of the cantilevered portion 106 for a given series resonance
frequency. As shown, there are relative maxima in Qs, at points 208,
209 and 210 and local minima at points 211, 212 and 213 as the width 109
increases. Notably, Qs improves significantly at a certain width
109, compared with width=0 of the cantilevered portion 106, which is
equivalent to an acoustic resonator having substantially the same
configuration as acoustic resonator 100 but without cantilevered portions
106.

[0048] As described above, the cantilevered portion 106 at the edge of
active area 110 of the acoustic resonator will reflect certain acoustic
modes due to the impedance mismatch at the boundary of the cantilevered
portion 106 and the active area 110, resulting in improved Q. It is
believed that the local minima may result from the excitation of a
mechanical resonance of the cantilevered portion 106, which results in
losses. The excited resonance conditions at relative minima (points 211,
212 and 213) result in energy not reflected back into the active area 110
of the acoustic resonator 100, losses and, therefore, reduced Q.
Accordingly, when designing acoustic resonator 100, the width 109 of the
cantilevered portion 106 is beneficially selected at a relative maximum
(points 208,209 or 210), and not at a relative minimum (points 211, 212
or 213).

[0049] Moreover, because the cantilevered portion 106 does not generate
spurious lateral modes, there is no attendant degradation in Q near the
series resonance frequency as can occur with the inclusion of known
raised frame elements (sometimes referred to as `outies`) and known
recessed frame elements (sometimes referred to as `innies`.) Notably,
both raised frame elements and recessed frame elements may be disposed
annularly about acoustic resonator and are sometimes referred to as
annular recesses and annular frames. The raised frame elements and
recessed frame elements may generate spurious modes, but recessed frame
elements improve the coupling coefficient (kt2), and raised
frame elements may slightly decrease kt2. Furthermore the
cantilevered portion 106 does not generate spurious modes because its
location is not within the active area 110. The cantilevered portion 106
also does not degrade kt2 as significantly as the raised and
recessed frame elements. As can be appreciated from a review of FIG. 2A,
kt2 at peak Q corresponds to a width of the cantilevered
portion 106 of approximately 4.75 μm is approximately 5.2. This
represents an increase in kt2 of approximately 10% greater than
that of a known acoustic resonator with a raised frame element.

[0050] FIG. 3 shows a cross-sectional view of an acoustic resonator 300 in
accordance with a representative embodiment. Many of the features of the
acoustic resonator 300 are common to those of acoustic resonator 100
described in connection with representative embodiments in FIGS. 1A-1B.
The details of common features, characteristics and benefits thereof are
not repeated in order to avoid obscuring the presently described
embodiments.

[0051] The acoustic resonator 300 comprises a bridge 301 along the
interconnection side 112. The bridge 301 provides a gap 302, which may be
avoid (e.g., air) or may be filled with a low acoustic impedance
material. The bridge 301 is described in the parent application (Ser. No.
12/490,525 entitled "ACOUSTIC RESONATOR STRUCTURE COMPRISING A BRIDGE"),
and as such many of the details of the bridge 301 are not repeated in the
present application to avoid obscuring the description of the
representative embodiments of the acoustic resonator 300.

[0052] As described above, the cantilevered portion 106 provides an
improvement in the Q-factor. Similarly, the bridge 301 also provides an
improvement in the Q-factor. Beneficially, the combination of the
cantilevered portion 106 and the bridge 301 provides a further
improvement in the Q-factor of the acoustic resonator 300. To this end,
inclusion of the bridge 301 with the cantilevered portion 106 in the
acoustic resonator 300 results in an improvement in the Q-factor at
parallel resonance (Qp) and some impact on the Q-factor at series
resonance (Qs). This is somewhat expected since the bridge 301
predominantly impacts Qp, as described in the parent application.

[0053] FIG. 4A shows a graph 400 of the Q-factor at parallel resonance
(Qp) versus width (e.g., width 109, (`wing width`)) of the cantilevered
portion 106 of an acoustic resonator comprising a bridge (e.g., acoustic
resonator 300) in accordance with a representative embodiment. The graph
400 provides data of an acoustic resonator comprising three cantilevered
portions 106, such as illustratively shown in FIGS. 1A and 1B. The
Q-factor is dependent on the wing width (e.g., width 109) for a given
parallel resonance frequency. As shown, there are relative maxima in
Qp at points 401, 402 and 403; and relative minima at points 404 and
405 as the width 109 increases. Notably, Qp improves significantly
at a certain width 109, compared with width=0 of the cantilevered portion
106, which is equivalent to an acoustic resonator having substantially
the same configuration shown in FIG. 3 but without cantilevered portions
106.

[0054] The synergistic impact of the combination of the bridge 301 and the
cantilevered portions 106 on Qp can be appreciated by a comparison of
data in FIGS. 2A and 4A. For example, in an embodiment comprising
cantilevered portion 106 having a width (e.g., width 109) of
approximately 2.5 μm, Qp FIG. 2A (near point 201, for example) is
approximately 850. By contrast, in an embodiment comprising bridge 301
and cantilevered portion 106 having a width of approximately 2.5 μm
(e.g., near point 406) provides Qp of approximately 1500. Similarly, in
an embodiment comprising cantilevered portion 106 having a width (e.g.,
width 109) of approximately 3.0 μm, Qp in FIG. 2A (near point 202, for
example) is approximately 975. By contrast, in an embodiment comprising
bridge 301 and cantilevered portion 106 having a width of approximately
3.0 μm provides Qp approximately 1750 (e.g., point 402 in FIG. 4A).

[0055] FIG. 4B shows a graph 407 of the Q-factor at series resonance
(Qs) versus width (e.g., width 109) of the cantilevered portion 106
of an acoustic resonator comprising a bridge (e.g., acoustic resonator
300) in accordance with a representative embodiment. The graph 407
provides data of an acoustic resonator comprising three cantilevered
portions 106, such as illustratively shown in FIGS. 1A and 1B. The
Q-factor is dependent on the wing width for a given series resonance
frequency. As shown, there are relative maxima in Qp at points 408,
409 and 410; and relative minima at points 411, 412, 413 and 414 as the
width 109 increases. Notably, Qs improves significantly at a certain
width 109, compared with width=0 of the cantilevered portion 106, which
is equivalent to an acoustic resonator having substantially the same
configuration shown in FIG. 3 but without cantilevered portions 106. As
note previously, the impact of the bridge 301 on improved Qs is less
dramatic than its impact on Qp.

[0056] FIG. 4C shows a graph of the Q-factor at parallel resonance
(Qp) versus width of the cantilevered portion(s) of an acoustic
resonator in accordance with a representative embodiment. As the total
thickness of the acoustic stack decreases, the resonance frequency
increases and, therefore, the acoustic wavelength at the resonance
frequency decreases. An optimum width 109 (`wing width`) of the
cantilevered portion 106, at which the most Q enhancement is achieved, is
determined by resonance acoustic quarter-wavelength, therefore smaller
optimum wing width is required to achieve optimum Q, Notably, FIG. 4C
relates to an acoustic resonator having a parallel resonance of 800 MHz.
A maximum Q-value (shown at point 415) is attained at a wing width of
approximately 1.6 μm.

[0057] FIG. 5A shows a cross-sectional view of an acoustic resonator 500
taken along line 5B-5B in accordance with a representative embodiment.
FIG. 5B shows atop view of the acoustic resonator 500. Many of the
features of the acoustic resonator 500 are common to those of acoustic
resonators 100, 300 described in connection with representative
embodiments in FIGS. 1A-1B and 3. The details of common features,
characteristics and benefits thereof are not repeated in order to avoid
obscuring the presently described embodiments.

[0058] The acoustic resonator 500 comprises the bridge 301 along the
interconnection side 112. The bridge 301 provides the gap 302, which may
be a void (e.g., air) or may be filled with a low acoustic impedance
material. In addition to the bridge 301, the acoustic resonator 500
comprises a raised frame element 501 (commonly referred to as an
`outie`). The raised frame element 501 may be provided over one or more
sides of the acoustic resonator 500 and provides an acoustic mismatch at
the boundary of the second electrode 104, thereby improving signal
reflections at the boundary and reducing acoustic tosses. Ultimately,
reduced losses translate into an improved Q-factor of the device. While
the raised frame element 501 are shown disposed over the second electrode
103, these features may instead be provided over the first electrode 102
and beneath the piezoelectric layer 103, or selectively on both the first
and second electrodes 102,104. Further details of the use, formation and
benefits of the raised frame element 501 may be found for example, in
commonly owned U.S. Pat. No. 7,280,007 entitled "Thin Film Bulk Acoustic
Resonator with a Mass Loaded Perimeter" to Feng, et al.; and commonly
owned U.S. Patent Application Publication 20070205850 entitled
"Piezoelectric Resonator Structure and Electronic Filters having Frame
Elements" to Jamneala, et al. The disclosures of this patent and patent
application publication are specifically incorporated herein by
reference.

[0059] The raised frame element 501 results in an increase in the parallel
impedance (Rp) but generates spurious modes below the series resonance
frequency; whereas the cantilevered portion 106 increases Rp without
degrading Qs. This is because the area of the raised frame element 501
represents a comparatively small fraction of the active area of the
acoustic resonator 500. It can be shown that this is equivalent to an
acoustic resonator connected in parallel to an acoustic resonator
comprising a frame element. Since the resonance frequency of an acoustic
resonator comprising the raised frame element 501 is lower, spurious
modes are generated below fs of the acoustic resonator without the
frame element. The addition of the cantilevered portion 106 to the
acoustic resonator 500 comprising the raised frame element 501 further
increases Rp without resulting in additional spurious modes below fs
because the wing 106 lies outside of the active area 110 of the acoustic
resonator 500.

[0060] FIG. 6 shows a cross-sectional view of an acoustic resonator 600 in
accordance with a representative embodiment. Many of the features of the
acoustic resonator 600 are common to those of acoustic resonators 100,
300, 500 described in connection with representative embodiments in FIGS.
1A-1B, 3, 5A and 5B. The details of common features, characteristics and
benefits thereof are not repeated in order to avoid obscuring the
presently described embodiments.

[0061] The acoustic resonator 600 comprises the bridge 301 along the
interconnection side 112. The bridge 301 provides the gap 302, which may
be a void (e.g., air) or may be filled with a low acoustic impedance
material. In addition to the bridge 301, the acoustic resonator 600
comprises a recessed frame element 601 (`innie`). The recessed frame
element 601 may be disposed along one or more sides of the acoustic
resonator 600 and provides an acoustic mismatch at the perimeter of the
second electrode 104, thereby improving signal reflections and reducing
acoustic tosses. Ultimately, reduced losses translate into an improved
Q-factor of the device. While the recessed frame element 601 is shown
disposed over the second electrode 104, the recessed frame element 601
may instead be provided over the first electrode 102 and beneath the
piezoelectric layer 103, or selectively on both the first and second
electrodes 102,104. Further details of the use, formation and benefits of
the recessed frame element 601 may be found for example, in commonly
owned U.S. Pat. No. 7,280,007 entitled "Thin Film Bulk Acoustic Resonator
with a Mass Loaded Perimeter" to Feng, et al.; and commonly owned U.S.
Patent Application Publication 20070205850 entitled "Piezoelectric
Resonator Structure and Electronic Filters having Frame Elements" to
Jamneala, et al. The disclosures of this patent and patent application
publication are specifically incorporated herein by reference. Moreover,
the incorporation of both a raised frame element (e.g., raised frame
element 501) and a recessed frame (e.g., recessed frame element 601) in
an acoustic resonator 100, 300, 500, 600 is also contemplated by the
present teachings. The incorporation of both raised and recessed frame
elements in an acoustic resonator is disclosed in the parent application
(U.S. patent application Ser. No. 12/490,525).

[0062] When connected in a selected topology, a plurality of acoustic
resonators 100, 300, 500, 600 can function as an electrical filter. FIG.
7 shows a simplified schematic block diagram of an electrical filter 700
in accordance with a representative embodiment. The electrical filter 700
comprises series acoustic resonators 701 and shunt acoustic resonators
702. The series acoustic resonators 701 and shunt acoustic resonators 702
may comprise the acoustic resonators 100, 300, 500, 600 described in
connection with the representative embodiments of FIGS. 1A, 1B, 3, 5A, 5B
and 6. The electrical filter 700 is commonly referred to as a ladder
filter, and may be used for example in duplexer applications. Further
details of a ladder-filter arrangement may be as described for example in
U.S. Pat. No. 5,910,756 to Ella, and U.S. Pat. No. 6,262,637 to Bradley,
et al. The disclosures of these patents are specifically incorporated by
reference. It is emphasized that the topology of the electrical filter
700 is merely illustrative and other topologies are contemplated.
Moreover, the acoustic resonators of the representative embodiments are
contemplated in a variety of applications besides duplexers.

[0063] In accordance with illustrative embodiments, acoustic resonators
for various applications such as in electrical filters are described
having an electrode comprising a cantilevered portion. Additionally,
acoustic resonators for various applications such as in electrical
fitters are described having an electrode comprising a cantilevered
portion and a bridge. One of ordinary skill in the art appreciates that
many variations that are in accordance with the present teachings are
possible and remain within the scope of the appended claims. These and
other variations would become clear to one of ordinary skill in the art
after inspection of the specification, drawings and claims herein. The
invention therefore is not to be restricted except within the spirit and
scope of the appended claims.